I believe there are some lever guns in pistol calibers(.357 & .44). I have hunted deer in heavy brush with a Ruger carbine in .44 mag. A .22 will kill a coyote,(even a wild hog), however, like anything else you must hit the right place. Depending on closeness, you might want a over/under type of scope mount, so if it's too close to see in the scope, you can still use the iron sights. I had a cousin who was squirrel hunting with a new pup and starteled a coyote. When the pup ran back to him the coyote followed. His only problem was it was too close to see in his scope, and he had trouble hitting it firing from the hip.
If hungry enough, rabid, scared, mating season, protecting it's territory, or just plain crazy enough, a wild animal can and will attack. It's why they are called wild animals. I've seen ads for a show on "Animal Planet", about people who have a wild animal for a pet and get into trouble when the animal does what comes naturally.